Certificate for #5190 ⟨a, b, c | aa=b, abcb=a⟩

Back:⟨a, b, c | aa=b, abcb=a⟩

Completion settings:

[1] b=aa

Axiom: aa=b.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2].

[2] aaacaa=a

Axiom: abcb=a.

Reduce LHS:

[1]a(b)cb
[1]⇒ aaac(b)
⇒ aaacaa

Referenced by [3], [4], [5].

[3] aacaa=aaaca

Overlap of [2] aaacaa=a with [2] aaacaa=a:

aaac aa aaacaa

Critical pair: aaaca=aacaa.

Flip LHS and RHS.

Referenced by [4], [5].

[4] acaa=aaca

Overlap of [2] aaacaa=a with [3] aacaa=aaaca:

aaac aa aacaa

Critical pair: aaacaaaca=acaa.

Reduce LHS:

[2](aaacaa)aca
⇒ aaca

Flip LHS and RHS.

Defines rule #1.

[5] aaaaca=a

Overlap of [2] aaacaa=a with [3] aacaa=aaaca:

a aacaa aacaa

Critical pair: aaaaca=a.

Defines rule #2.